Finite Group Databasebeta

← #35311490

Subgroups — #35311490

Order 21248.

1018 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24916026C211yesmaximal, characteristic, complemented
2C2×#19127665C211yesmaximal, characteristic
3#24909846C211yesmaximal, characteristic
4C2×#19127473C211yesmaximal, characteristic, complemented
5C2×#19127472C211yesmaximal, characteristic, complemented
6#24907201C211yesmaximal, characteristic, complemented
7C2×#407×C83C211yesmaximal, characteristic
8C22×#13050574C2211yescharacteristic
9C22×#13050574C2211yescharacteristic
10C2×#14581751C2211yescharacteristic
11C2×#14581751C2211yescharacteristic
12#19127729—22no—
13#19127727—22no—
14#19127724—22no—
15#19127665—22no—
16#19127665—22no—
17C2×C22⋊(C83⋊C8)—22no—
18#19127564C412yes—
19#19127561—22no—
20#19127557C412yes—
21C4×C22⋊Dic83—22no—
22#19127473—22no—
23#19127472—22no—
24#19127469—22no—
25C24×C4×C83C2211yescharacteristic
26C22×M16×C83C2211yescharacteristic
27C22×M16×C83C2211yescharacteristic
28#407×C83—22no—
29#407×C83—22no—
30C2×C22⋊C8×C83—22no—
31C2×#13050574—21no—
32C2×#13050574—21no—
33C2×#13050574—21no—
34C2×#13050574—21no—
35C2×#13050574—21no—
36C2×#13050574—21no—
37C2×#13050574—21no—
38C2×#13050574—21no—
39C2×#13050574—21no—
40C2×#13050574—21no—
41C2×#13050574—21no—
42C2×#13050574D412yes—
43C22×C83⋊C8—21no—
44C22×C83⋊C8D412yes—
45#14581751—21no—
46#14581751—21no—
47#14581751—21no—
48#14581751—21no—
49#14581751—21no—
50#14581751—21no—
51#14581751—21no—
52#14581751—21no—
53C2×C4⋊Dic83—21no—
54C2×C4⋊Dic83D412yes—
55C2×C22⋊Dic83—24no—
56C2×C22⋊Dic83C2×C412yes—
57C2×C22⋊Dic83C2×C412yes—
58C2×C4×Dic83—21no—
59C2×C4×Dic83D412yes—
60Dic83⋊C8—28no—
61C22⋊(C83⋊C8)—28no—
62C83⋊#95—24no—
63C25×C83C2×C411yescharacteristic
64C23×C4×C83—21no—
65C23×C4×C83—21no—
66C23×C4×C83—21no—
67C23×C4×C83—21no—
68C23×C4×C83—21no—
69C23×C4×C83—21no—
70C23×C4×C83—21no—
71C23×C4×C83—21no—
72C23×C4×C83—21no—
73C23×C4×C83—21no—
74C23×C4×C83—21no—
75C23×C4×C83—21no—
76C23×C4×C83C2×C411yescharacteristic
77C23×C4×C83D412yes—
78C23×C4×C83Q812yes—
79C23×C4×C83C2311yescharacteristic
80C2×M16×C83—21no—
81C2×M16×C83—21no—
82C2×M16×C83—21no—
83C2×M16×C83—21no—
84C2×M16×C83—21no—
85C2×M16×C83—21no—
86C2×M16×C83—21no—
87C2×M16×C83—21no—
88C2×M16×C83—21no—
89C2×M16×C83—21no—
90C2×M16×C83—21no—
91C2×M16×C83D412yes—
92C22×C8×C83—21no—
93C22×C8×C83D412yes—
94C22⋊C8×C83—28no—
95C22×Dic83—22no—
96C22×Dic83C22⋊C414yes—
97#13050574—22no—
98#13050574—22no—
99#13050574—41no—
100#13050574—41no—
101#13050574—41no—
102#13050574—41no—
103#13050574—41no—
104#13050574—41no—
105C2×C83⋊C8—22no—
106C2×C83⋊C8—22no—
107C2×C83⋊C8—22no—
108C2×C83⋊C8—22no—
109C2×C83⋊C8—41no—
110C2×C83⋊C8—41no—
111C4⋊Dic83—22no—
112C4⋊Dic83—22no—
113C4⋊Dic83—41no—
114C4⋊Dic83—41no—
115C22⋊Dic83—22no—
116C22⋊Dic83—22no—
117C22⋊Dic83—22no—
118C22⋊Dic83—22no—
119C22⋊Dic83—48no—
120C4×Dic83—22no—
121C4×Dic83—22no—
122C4×Dic83—41no—
123C4×Dic83—41no—
124C24×C83—21no—
125C24×C83—21no—
126C24×C83—21no—
127C24×C83—21no—
128C24×C83—21no—
129C24×C83—21no—
130C24×C83—44no—
131C24×C83C4⋊C412yes—
132C24×C83C22×C411yescharacteristic
133C22×C4×C83—21no—
134C22×C4×C83—21no—
135C22×C4×C83—21no—
136C22×C4×C83—21no—
137C22×C4×C83—21no—
138C22×C4×C83—21no—
139C22×C4×C83—22no—
140C22×C4×C83—22no—
141C22×C4×C83—22no—
142C22×C4×C83—22no—
143C22×C4×C83—22no—
144C22×C4×C83—22no—
145C22×C4×C83—22no—
146C22×C4×C83—22no—
147C22×C4×C83—22no—
148C22×C4×C83—22no—
149C22×C4×C83—22no—
150C22×C4×C83—22no—
151C22×C4×C83—41no—
152C22×C4×C83—41no—
153C22×C4×C83—41no—
154C22×C4×C83—41no—
155C22×C4×C83—41no—
156C22×C4×C83—41no—
157C22×C4×C83—41no—
158C22×C4×C83—41no—
159C22×C4×C83—41no—
160C22×C4×C83—41no—
161C22×C4×C83—41no—
162C22×C4×C83—41no—
163C22×C4×C83—41no—
164C22×C4×C83—41no—
165C22×C4×C83—41no—
166C22×C4×C83—41no—
167C22×C4×C83C4⋊C412yes—
168C22×C4×C83C2×D411yescharacteristic
169C22×C4×C83C2×D411yescharacteristic
170C22×C4×C83C2×D411yescharacteristic
171C22×C4×C83C2×D411yescharacteristic
172C22×C4×C83C2×D411yescharacteristic
173C22×C4×C83C2×D411yescharacteristic
174C22×C4×C83C2×D411yescharacteristic
175C22×C4×C83C2×Q811yescharacteristic
176C22×C4×C83#4111yescharacteristic
177C22×C4×C83#4111yescharacteristic
178C22×C4×C83#4111yescharacteristic
179C22×C4×C83#4111yescharacteristic
180C22×C4×C83#4111yescharacteristic
181C22×C4×C83#4111yescharacteristic
182M16×C83—22no—
183M16×C83—22no—
184M16×C83—41no—
185M16×C83—41no—
186M16×C83—41no—
187M16×C83—41no—
188M16×C83—41no—
189M16×C83—41no—
190C2×C8×C83—22no—
191C2×C8×C83—22no—
192C2×C8×C83—22no—
193C2×C8×C83—22no—
194C2×C8×C83—41no—
195C2×C8×C83—41no—
196C23×C83—24no—
197C23×C83—24no—
198C23×C83—24no—
199C23×C83—22no—
200C23×C83—22no—
201C23×C83—22no—
202C23×C83—44no—
203C23×C83—42no—
204C23×C83—42no—
205C23×C83—42no—
206C23×C83—42no—
207C23×C83—44no—
208C23×C83—44no—
209C23×C83—44no—
210C23×C83—41no—
211C23×C83—41no—
212C23×C83—41no—
213C23×C83—41no—
214C23×C83C2×C22⋊C411yescharacteristic
215C23×C83C2×C4⋊C411yescharacteristic
216C23×C83#11711yescharacteristic
217C23×C83C4×D411yescharacteristic
218C23×C83C4×D411yescharacteristic
219C23×C83C4×D411yescharacteristic
220C23×C83C4×D411yescharacteristic
221C2×C4×C83—22no—
222C2×C4×C83—22no—
223C2×C4×C83—22no—
224C2×C4×C83—41no—
225C2×C4×C83—41no—
226C2×C4×C83—41no—
227C2×C4×C83—41no—
228C2×C4×C83—42no—
229C2×C4×C83—42no—
230C2×C4×C83—42no—
231C2×C4×C83—42no—
232C2×C4×C83—42no—
233C2×C4×C83—42no—
234C2×C4×C83—42no—
235C2×C4×C83—42no—
236C2×C4×C83#12011yescharacteristic
237C2×C4×C83#12011yescharacteristic
238C2×C4×C83#12011yescharacteristic
239C2×C4×C83#12111yescharacteristic
240C2×C4×C83#12111yescharacteristic
241C2×C4×C83#12111yescharacteristic
242C2×C4×C83#12111yescharacteristic
243C2×C4×C83#12111yescharacteristic
244C2×C4×C83#12111yescharacteristic
245C2×C4×C83#12111yescharacteristic
246C2×C4×C83#12111yescharacteristic
247C2×C4×C83C22⋊Q811yescharacteristic
248C2×C4×C83C22⋊Q811yescharacteristic
249C2×C4×C83C22⋊Q811yescharacteristic
250C2×C4×C83C22⋊Q811yescharacteristic
251C2×C4×C83C22⋊Q811yescharacteristic
252C2×C4×C83C22⋊Q811yescharacteristic
253C2×C4×C83#12311yescharacteristic
254C2×C4×C83#12311yescharacteristic
255C2×C4×C83#12311yescharacteristic
256C2×C4×C83#12311yescharacteristic
257C2×C4×C83#12311yescharacteristic
258C2×C4×C83#12411yescharacteristic
259C2×C4×C83#12411yescharacteristic
260C2×C4×C83#12411yescharacteristic
261C2×C4×C83#12611yescharacteristic
262C2×C4×C83#12611yescharacteristic
263C2×C4×C83#12711yescharacteristic
264C2×Dic83—24no—
265C2×Dic83—44no—
266C2×Dic83—44no—
267C2×Dic83—42no—
268C8×C83—42no—
269C8×C83—42no—
270C83⋊C8—42no—
271C83⋊C8—42no—
272C22×C83—22no—
273C22×C83—22no—
274C22×C83—22no—
275C22×C83—24no—
276C22×C83—24no—
277C22×C83—24no—
278C22×C83—41no—
279C22×C83—41no—
280C22×C83—41no—
281C22×C83—41no—
282C22×C83—44no—
283C22×C83—42no—
284C22×C83—42no—
285C22×C83—42no—
286C22×C83—44no—
287C22×C83—44no—
288C22×C83—44no—
289C22×C83—42no—
290C22×C83#38011yescharacteristic
291C22×C83#38511yescharacteristic
292C22×C83#38511yescharacteristic
293C22×C83#38611yescharacteristic
294C22×C83#38811yescharacteristic
295C22×C83#38811yescharacteristic
296C22×C83#39011yescharacteristic
297C4×C83—42no—
298C4×C83#39211yescharacteristic
299C4×C83#39311yescharacteristic
300C4×C83#39411yescharacteristic
301C4×C83#39411yescharacteristic
302C4×C83#39611yescharacteristic
303C4×C83#39611yescharacteristic
304C4×C83#39711yescharacteristic
305C4×C83#39911yescharacteristic
306Dic83—44no—
307Dic83—82no—
308#11071—831nomaximal, Sylow
309C2×C83—21no—
310C2×C83—21no—
311C2×C83—21no—
312C2×C83—21no—
313C2×C83—21no—
314C2×C83—21no—
315C2×C83—44no—
316C2×C83#143911yescharacteristic
317C2×C83#189112yes—
318#2905—831no—
319C2×#407—831no—
320C2×#407D8311yescharacteristic
321#2280—831no—
322C2×#344—831no—
323C2×#344—831no—
324#1742—831no—
325C83#1107111yescharacteristic, complemented, Sylow
326C24×C4C2×D8311yescharacteristic
327C22×M16—831no—
328C22×M16—831no—
329C22×M16C2×D8311yescharacteristic
330C22×M16C2×D8311yescharacteristic
331C2×#117—831no—
332C2×#117—831no—
333#424—1662no—
334#424—1662no—
335#423—1662no—
336#407—22no—
337#407—22no—
338#407—1662no—
339#407—1662no—
340C2×C22⋊C8—22no—
341C2×C22⋊C8—1662no—
342#381—832no—
343#380—1662no—
344#379—832no—
345C4×C22⋊C4—1662no—
346#344—1662no—
347#344—1662no—
348#343—1662no—
349C25C4×D8311yescharacteristic
350C23×C4—21no—
351C23×C4—21no—
352C23×C4—21no—
353C23×C4—21no—
354C23×C4—21no—
355C23×C4—21no—
356C23×C4—21no—
357C23×C4—21no—
358C23×C4—21no—
359C23×C4—21no—
360C23×C4—21no—
361C23×C4—21no—
362C23×C4Dic16612yes—
363C23×C4C4×D8311yescharacteristic
364C23×C4C22⋊D8312yes—
365C23×C4C22×D8311yescharacteristic
366C2×M16—21no—
367C2×M16—21no—
368C2×M16—21no—
369C2×M16—21no—
370C2×M16—21no—
371C2×M16—21no—
372C2×M16—21no—
373C2×M16—21no—
374C2×M16—21no—
375C2×M16—21no—
376C2×M16—21no—
377C2×M16—832no—
378C2×M16—1661no—
379C2×M16—1661no—
380C2×M16—1661no—
381C2×M16—1661no—
382C2×M16—1661no—
383C2×M16—1661no—
384C2×M16—1661no—
385C2×M16—1661no—
386C2×M16—1661no—
387C2×M16—1661no—
388C2×M16—1661no—
389C2×M16C22⋊D8312yes—
390C22×C8—21no—
391C22×C8—832no—
392C22×C8—1661no—
393C22×C8C22⋊D8312yes—
394#117—1661no—
395#117—1661no—
396#117—1661no—
397#117—1661no—
398#117—1661no—
399#117—1661no—
400#117—1661no—
401#117—1661no—
402C2×C4⋊C4—832no—
403C2×C4⋊C4—1661no—
404C2×C22⋊C4—832no—
405C2×C22⋊C4—832no—
406C2×C22⋊C4—1664no—
407C2×C42—832no—
408C2×C42—1661no—
409C4⋊C8—1668no—
410C22⋊C8—28no—
411C22⋊C8—1668no—
412#95—1664no—
413C24—21no—
414C24—21no—
415C24—21no—
416C24—21no—
417C24—21no—
418C24—21no—
419C24—44no—
420C24Dic83⋊C412yes—
421C24C2×C4×D8311yescharacteristic
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—41no—
441C22×C4—41no—
442C22×C4—41no—
443C22×C4—41no—
444C22×C4—41no—
445C22×C4—41no—
446C22×C4—41no—
447C22×C4—41no—
448C22×C4—41no—
449C22×C4—41no—
450C22×C4—41no—
451C22×C4—41no—
452C22×C4—41no—
453C22×C4—41no—
454C22×C4—41no—
455C22×C4—41no—
456C22×C4—834no—
457C22×C4—1662no—
458C22×C4Dic83⋊C412yes—
459C22×C4D4×D8311yescharacteristic
460C22×C4D4×D8311yescharacteristic
461C22×C4D4×D8311yescharacteristic
462C22×C4D4×D8311yescharacteristic
463C22×C4C2×C22⋊D8311yescharacteristic
464C22×C4C2×C22⋊D8311yescharacteristic
465C22×C4C2×C22⋊D8311yescharacteristic
466C22×C4C2×Dic16611yescharacteristic
467C22×C4#1305058911yescharacteristic
468C22×C4#1305058911yescharacteristic
469C22×C4#1305058911yescharacteristic
470C22×C4#1305058911yescharacteristic
471C22×C4#1305059011yescharacteristic
472C22×C4#1305059011yescharacteristic
473M16—22no—
474M16—22no—
475M16—41no—
476M16—41no—
477M16—41no—
478M16—41no—
479M16—41no—
480M16—41no—
481M16—3321no—
482M16—3321no—
483M16—3321no—
484M16—3321no—
485M16—3321no—
486M16—3321no—
487M16—1662no—
488M16—1662no—
489C2×C8—22no—
490C2×C8—22no—
491C2×C8—22no—
492C2×C8—22no—
493C2×C8—41no—
494C2×C8—41no—
495C2×C8—3321no—
496C2×C8—3321no—
497C2×C8—1662no—
498C2×C8—1662no—
499C2×C8—1662no—
500C2×C8—1662no—
501C4⋊C4—3321no—
502C4⋊C4—3321no—
503C4⋊C4—1662no—
504C4⋊C4—1662no—
505C22⋊C4—3328no—
506C22⋊C4—1662no—
507C22⋊C4—1662no—
508C22⋊C4—1662no—
509C22⋊C4—1662no—
510C42—3321no—
511C42—3321no—
512C42—1662no—
513C42—1662no—
514C23—24no—
515C23—24no—
516C23—24no—
517C23—22no—
518C23—22no—
519C23—22no—
520C23—44no—
521C23—42no—
522C23—42no—
523C23—42no—
524C23—42no—
525C23—44no—
526C23—44no—
527C23—44no—
528C23—41no—
529C23—41no—
530C23—41no—
531C23—41no—
532C23C22⋊C4×D8311yescharacteristic
533C23C2×Dic83⋊C411yescharacteristic
534C23#1458174811yescharacteristic
535C23(C22⋊D83)⋊C411yescharacteristic
536C23(C22⋊D83)⋊C411yescharacteristic
537C23C4×C22⋊D8311yescharacteristic
538C23C4×C22⋊D8311yescharacteristic
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—3324no—
555C2×C4—3324no—
556C2×C4—3322no—
557C2×C4—1664no—
558C2×C4#1458176011yescharacteristic
559C2×C4#1458176011yescharacteristic
560C2×C4#1458176111yescharacteristic
561C2×C4#1458176311yescharacteristic
562C2×C4#1458176311yescharacteristic
563C2×C4#1458176411yescharacteristic
564C2×C4#1458176411yescharacteristic
565C2×C4#1458176411yescharacteristic
566C2×C4#1458176411yescharacteristic
567C2×C4#1458176511yescharacteristic
568C2×C4#1458176511yescharacteristic
569C2×C4#1458176911yescharacteristic
570C2×C4#1458176911yescharacteristic
571C2×C4#1458176911yescharacteristic
572C2×C4#1458176911yescharacteristic
573C2×C4#1458177111yescharacteristic
574C2×C4#1458177111yescharacteristic
575C2×C4#1458177311yescharacteristic
576C2×C4#1458177311yescharacteristic
577C2×C4#1458177411yescharacteristic
578C2×C4#1458177411yescharacteristic
579C2×C4#1458177511yescharacteristic
580C2×C4#1458177811yescharacteristic
581C2×C4#1458177811yescharacteristic
582C2×C4#1458177911yescharacteristic
583C2×C4#1458178511yescharacteristic
584C2×C4#1458178511yescharacteristic
585C2×C4#1458178811yescharacteristic
586C8—42no—
587C8—42no—
588C8—3322no—
589C8—3322no—
590C22—22no—
591C22—22no—
592C22—22no—
593C22—24no—
594C22—24no—
595C22—24no—
596C22—41no—
597C22—41no—
598C22—41no—
599C22—41no—
600C22—44no—
601C22—42no—
602C22—42no—
603C22—42no—
604C22—44no—
605C22—44no—
606C22—44no—
607C22—42no—
608C22#1912755911yescharacteristic
609C22#1912757311yescharacteristic
610C22#1912757411yescharacteristic
611C22#1912757711yescharacteristic
612C22#1912758911yescharacteristic
613C22#1912759511yescharacteristic
614C22#1912760111yescharacteristic
615C4—42no—
616C4—3324no—
617C4—6642no—
618C4#1912760911yescharacteristic
619C4#1912761311yescharacteristic
620C4#1912761511yescharacteristic
621C4#1912761611yescharacteristic
622C4#1912762411yescharacteristic
623C4#1912762411yescharacteristic
624C4#1912762911yescharacteristic
625C4#1912763711yescharacteristic
626C2—21no—
627C2—21no—
628C2—21no—
629C2—21no—
630C2—21no—
631C2—21no—
632C2—44no—
633C2#2490570611yescharacteristic
634C2#2490787812yes—
subgroupG/H
centerC2×C4#14581760
commutatorC24×C83C22×C4
FrattiniC23×C4C22×D83
FittingC2×#407×C83C2
socleC22×C83#386
prime radicalC25×C83C2×C4
cosocleC23×C4×C83C23
hypercenterC2×#407D83
hypocenterC83#11071
LCSG ▷ C24×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#407

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #24916026C2semidirect
4. C2×#19127473C2semidirect
5. C2×#19127472C2semidirect
6. #24907201C2semidirect
325. C83#11071semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#249160262
C2×#191276652
#249098462
C2×#191274732
C2×#191274722
#249072012
C2×#407×C832
#1107183